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Domination in graphs with minimum degree two

✍ Scribed by William McCuaig; Bruce Shepherd

Publisher: John Wiley and Sons
Year: 1989
Tongue: English
Weight: 545 KB
Volume: 13
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190130610

No coin nor oath required. For personal study only.

✦ Synopsis

The domination number y ( G ) of a graph G = (V E ) is the minimum cardinality of a subset of Vsuch that every vertex is either in the set or is adjacent to some vertex in the set. We show that if a connected graph G has minimum2degree two and is not one of seven exceptional graphs, then y ( g ) I ~l V l .

We also characterize those connected graphs with y ( G ) = FJVI.

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